We show that in the presense of disruptive selection, spatial distributions of sexually reproducing organisms with local mating neighborhoods give rise to symmetry breaking and spontaneous pattern formation in the genetic composition of local populations. Global dynamics follows conventional coarsening of systems with non-conserved order parameters in statistical physics. These patterns interact with boundary and internal barrier structures so as to generate counter-intuitive increases in diversity in patches with high perimeter-to-core ratios. The results have significant implications for the creation and maintenance of biological diversity and species formation.